Search Results for author: Ahmad Peyvan

Found 4 papers, 1 papers with code

Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity

no code implementations29 May 2024 Benjamin Shih, Ahmad Peyvan, Zhongqiang Zhang, George Em Karniadakis

Transformers have not been used in that capacity, and specifically, they have not been tested for solutions of PDEs with low regularity.

Operator learning

RiemannONets: Interpretable Neural Operators for Riemann Problems

1 code implementation16 Jan 2024 Ahmad Peyvan, Vivek Oommen, Ameya D. Jagtap, George Em Karniadakis

Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis.

Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)

no code implementations18 Jul 2023 Oded Ovadia, Vivek Oommen, Adar Kahana, Ahmad Peyvan, Eli Turkel, George Em Karniadakis

The proposed method, named Diffusion-inspired Temporal Transformer Operator (DiTTO), is inspired by latent diffusion models and their conditioning mechanism, which we use to incorporate the temporal evolution of the PDE, in combination with elements from the transformer architecture to improve its capabilities.

Operator learning Super-Resolution

Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils

no code implementations2 Feb 2023 Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, George Em Karniadakis

Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications.

regression

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